This invention relates to magnetic field correction devices (i.e., passive shim arrangements) for correcting the magnetic field generated by a magnet for producing a uniform field in magnetic resonance imaging devices, etc.
Generally, the magnets for producing a uniform magnetic field are designed to generate a homogeneous field by itself. However, due to working errors and effects of iron bodies in the neighborhood, it is difficult to attain the designed level of a uniform field. Thus, a magnetic field correction device, i.e., passive shim arrangement, is provided in the magnet for compensating for the working errors and effects of the iron bodies.
FIG. 7 is a perspective view of a conventional magnetic resonance imaging device for generating a uniform magnetic field. A magnet housing accommodates a solenoid coil (not shown) for generating a homogeneous magnetic field. On top of the magnet housing 1 is provided a port 2 which incorporates terminals (not shown) for supplying excitation current to the coil. Upon receiving the current supplied via the port 2, the coil generates a homogeneous field in the magnetic field region 3 within the magnet housing 1.
A plurality of non-magnetic shim holder tubes 4 are attached to the interior surface of the support cylinder 10 disposed within the magnetic housing 1. A magnetic shim element 5 for correcting the field is inserted in each one of the non-magnetic shim holder tubes 4. Each magnetic shim element 5 consists, for example, of a pair of magnetic bars of distinct lengths soldered to each other. The two ends of the non-magnetic shim holder tubes 4 are sealed by the stoppers 6. The magnetic field correction device consists of the non-magnetic shim holder tubes 4, the magnetic shim elements 5 and the stoppers 6.
Next the operation of the device of FIG. 7 is described. FIG. 8 is a perspective view of a single magnetic bar, two of which of distinct lengths are soldered to each other to form a magnetic shim element. The bar is axially aligned with the Z-axis. The magnetization of the magnetic bar 11 is saturated by means of the external magnetic field 12 along the Z-axis. As a result, magnetic charges appear at the end surfaces 11a and 11b, such that a correction field 13 opposite to the external magnetic field 12 is generated. The magnetic shim elements 5 each consisting of two magnetic bars 11 of appropriate dimensions thus obtained are disposed at appropriate positions upon the interior surface of the support cylinder 10 within the bore of the magnet housing 1, such that the non-homogeniety of the magnetic field within the magnetic field region 3 is corrected.
Next, the details of the correction of the magnetic field are described. FIG. 9 is a schematic axial sectional view of a single magnetic bar, showing the positional relation between the magnetic bar and the measurement point in the Z-Y plane. (The Z-axis agrees with the axis of the support cylinder 10 and the field generating cylinder, and the origin is at the center of the magnetic field region 3.) FIG. 10 is a schematic end view of a single magnetic bar, showing the positional relation between the magnetic bar and the measurement point in the X-Y plane (the plane passing the origin and perpendicular to the Z-axis). The magnetic bar 11 is disposed parallel to the Z-axis at a circumferential attachment angle .phi. and an attachment radius a (see FIG. 10) such that the end surfaces of the magnetic bar 11 form end angles .alpha..sub.1, .alpha..sub.2 with respect to the origin and the Z-axis (see FIG. 9). The measurement point P is positioned at a radius r which forms an angle .phi. with respect to the X-axis (see FIG. 10) and angle .phi. with respect to the Z-axis (see FIG. 9).
Then, the magnetic field B.sub.z formed by the magnetic bar 11 at measurement point P is given by equation (1): ##EQU1## where K is a constant determined by the magnetic characteristic of the magnetic shim element 5, A is the cross-sectional area of the magnetic bar 11, .epsilon..sub.m is the Neumann coefficient (.epsilon..sub.m =2 if m.noteq.0 and .epsilon..sub.m =1 if m=0), and P.sub.n.sup.m is the associated Legendre polynomial of degree n and order m.
Further, the following table 1 shows the output components of the magnetic field in the spherical polar coordinates B.sub.z.sup.nm (up to n=2) together with the components expressed in the orthogonal coordinate system X, Y, Z.
TABLE 1 ______________________________________ (CORRESPONDENCE UP TO n = 2) COMPONENTS IN ORTHOGONAL n m COORDINATES ______________________________________ 1 0 Z 1 1 X or Y 2 0 Z.sup.2 2 1 ZX or ZY 2 2 X.sup.2 - Y.sup.2 or XY ______________________________________
Next, the magnetic field correction generating a negative X component with respect to the orthogonal coordinate system is described. As shown in equation (1), the number of the magnetic components generated by the magnetic bar 11 is infinite. However, since generally a&gt;r holds, the factor: (r/a).sup.n becomes negligibly small for those terms for which the value of n is great. Thus, it suffices to determine the dimensions and positions of the magnetic bars 11 which generate only the B.sub.z.sup.11 corresponding to the X-component among those components for which the values of n and m are small: B.sub.z.sup.11, B.sub.z.sup.21, B.sub.z.sup.22, B.sub.z.sup.31, B.sub.z.sup.32, B.sub.z.sup.33, B.sub.z.sup.41, B.sub.z.sup.42, B.sub.z.sup.43, B.sub.z.sup.44, B.sub.z.sup.51, B.sub.z.sup.52, B.sub.z.sup.53, B.sub.z.sup.54. This is effected as described below in (i), (ii), and (iii).
(i) The circumferential attachment angle .phi. of the magnetic bar 11 is determined as given by equations (2) through (9): EQU .phi.=(.pi./2)((1/2)+(1/3)+(1/4)) (2) EQU .phi.=(.pi./2)((1/2)+(1/3)-(1/4)) (3) EQU .phi.=(.pi./2)((1/2)-(1/3)+(1/4)) (4) EQU .phi.=(.pi./2)((1/2)-(1/3)-(1/4)) (5) EQU .phi.=(.pi./2)(-(1/2)+(1/3)+(1/4)) (6) EQU .phi.=(.pi./2)(-(1/2)+(1/3)-(1/4)) (7) EQU .phi.=(.pi./2)(-(1/2)-(1/3)+(1/4)) (8) EQU .phi.=(.pi./2)(-(1/2)-(1/3)-(1/4)) (9)
such that the factor: cos m(.PHI.-.phi.) for m=2, 3, 4 vanishes and thus the components: B.sub.z.sup.22, B.sub.z.sup.32, B.sub.z.sup.33, B.sub.z.sup.42, B.sub.z.sup.43, B.sub.z.sup.44, B.sub.z.sup.52, B.sub.z.sup.53, and B.sub.z.sup.54 vanish. On the other hand, the component B.sub.z.sup.11 corresponding to negative X-component is generated.
(ii) The end angles .alpha..sub.1, .alpha..sub.2 of each magnetic bar 11 are selected such that they satisfy: .alpha..sub.2 =.pi.-.alpha..sub.1. Then, the following equations (10) and (11) hold and the components B.sub.z.sup.21 and B.sub.z.sup.41 vanish: ##EQU2##
Further, by selecting the end angles .alpha..sub.1, .alpha..sub.2 of the two magnetic bars 11 at 33.88.degree. and 146.12.degree., respectively, or at 62.04.degree. and 117.96.degree., respectively, the components B.sub.z.sup.51 of the two magnetic bars are both eliminated.
(iii) If the cross-sectional area of the magnetic bar 11 having end angles .alpha..sub.1, .alpha..sub.2 at 33.88.degree. and 146.12.degree. respectively, and that of the magnetic bar 11 having end angles .alpha..sub.1, .alpha..sub.2 at 62.04.degree. and 117.96.degree. respectively, are represented by A.sub.1 and A.sub.2, respectively, then the resultant component B.sub.z.sup.31 of the two magnetic bars 11 is given by: EQU B.sub.z.sup.31 .varies.A.sub.1 {P.sub.4.sup.1 (cos 33.88.degree.)(sin 33.88.degree.).sup.5 }+A.sub.2 {P.sub.4.sup.1 (cos 62.04.degree.)(sin 62.04.degree.).sup.5 } (12)
Thus, by selecting the ratio A.sub.1 /A.sub.2 at 7.16 as shown by the following equation (13), the component B.sub.z.sup.31 vanishes. ##EQU3##
The position of the magnetic bar 11 and the ratio of the cross-sectional areas A.sub.1 /A.sub.2 of the two magnetic bars 11 are selected as described above in (i), (ii), and (iii) such that the components other than the desired component B.sub.z.sup.11 are eliminated.
The two magnetic bars 11 whose dimension and position are determined as described above are secured to each other by means of solder 14, etc., such that the relative axial position of the two bars is fixed. The two bars 11 thus secured to each other constitutes a magnetic shim element 5. Further, predetermined number of magnetic shim elements 5 are inserted into respective non-magnetic shim holder tubes 4 disposed at the attachment angle .phi. as determined by equations (2) through (9) in (i) above, and the homogeneity of the X-component of the magnetic field is thereby adjusted. By the way, the cross-sectional areas of the magnetic bars 11 are varied in accordance with the magnitude of the necessary field correction, although the ratio of the cross sectional areas of the two magnetic bars 11 is maintained at the value as determined in (iii).
The above field correction device still has the following disadvantage. The two magnetic bars 11 must first be secured to each other by means, for example, of the solder 14. This requires time and labor. Further, when a plurality of magnetic shim elements 5 are inserted into a non-magnetic shim holder tube 4, the shorter magnetic bar 11 of the firstly inserted magnetic shim element 5 obstructs the smooth entrance of the secondly inserted magnetic shim element 5. This increases the time and labor required for the insertion of the magnetic shim element 5 into the non-magnetic shim holder tubes 4.